Field theory with the Maxima computer algebra system

TL;DR

This paper demonstrates how the Maxima computer algebra system, with its add-on package itensor, can be used to develop a Lagrangian field theory and derive Maxwell's equations, showcasing its capabilities in symbolic physics computations.

Contribution

It introduces the use of Maxima and itensor for symbolic derivation of field equations, exemplified by Maxwell's equations, highlighting its application in theoretical physics.

Findings

Successfully derived Maxwell's equations from the Lagrangian using Maxima.

Showcased the derivation of conservation laws within the system.

Validated Maxima's utility in symbolic field theory computations.

Abstract

The Maxima computer algebra system, the open-source successor to MACSYMA, the first general-purpose computer algebra system that was initially developed at the Massachusetts Institute of Technology in the late 1960s and later distributed by the United States Department of Energy, has some remarkable capabilities, some of which are implemented in the form of add-on, "share" packages that are distributed along with the core Maxima system. One such share package is itensor, for indicial tensor manipulation. One of the more remarkable features of itensor is functional differentiation. Through this, it is possible to use itensor to develop a Lagrangian field theory and derive the corresponding field equations. In the present note, we demonstrate this capability by deriving Maxwell's equations from the Maxwell Lagrangian, and exploring the properties of the system, including current conservation.